a teacher needs to select 3 books from a shelf of 8 books. how many different sets of books can the teacher…

Explanation:

Step1: Identify combination formula

The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items, and $r$ is the number of items to be chosen. Here, $n = 8$ and $r=3$.

Step2: Calculate factorial values

$n!=8! = 8\times7\times6\times5\times4\times3\times2\times1$, $r!=3!=3\times2\times1$, and $(n - r)!=(8 - 3)!=5!=5\times4\times3\times2\times1$. Then $C(8,3)=\frac{8!}{3!(8 - 3)!}=\frac{8!}{3!5!}=\frac{8\times7\times6\times5!}{3\times2\times1\times5!}$.

Step3: Simplify the expression

Cancel out the $5!$ terms. We get $\frac{8\times7\times6}{3\times2\times1}=\frac{336}{6}=56$.

Answer:

A. 56